Idek if anyone's on this site anymore, but here's my problem (i guess ill do 20 points):

prove that (16^3-8^3)(4^3+2^3) is divisible by 63.

show steps

To be divisible by 63, it must be divisible by both 7 and 9, since 7x9 = 63.  Factor the expression, simplify, and see if both 7 and 9 are factors, which would make it divisible by both 7 and 9. (163 - 83)(43 + 23) = [(24)3 - (23)3] [(22)3 + 23] = (212 - 29)(26 + 23) = [29(23 - 1)] [23(23 + 1)] = [29(8 - 1)] [23(8 + 1)] = 29(7) 23 (9) = 63(212) It is a multiple of 63, and hence divisible by 63.